{
 "cells": [
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Assembly of the Biot equations\n",
    "\n",
    "In this tutorial we demonstrate how to assemble and solve the multi-physics Biot problem in PorePy. This tutorial will focus on a 2d domain. However, most of the code works for 1d, 2d, and 3d domains.<br>\n",
    "\n",
    "Let $\\Omega$ be a regular domain with boundary $\\partial \\Omega$. We indicate the outward unit normal vector of $\\partial \\Omega$ by $\\mathbf{n}$.<br>\n",
    "The Biot equations formulation read:\n",
    "$$ \\nabla \\cdot \\frac{1}{2}D(\\nabla \\mathbf{u} + \\nabla \\mathbf{u}^T) - \\alpha \\nabla p = F \\\\\n",
    "\\frac{\\partial}{\\partial t}(\\beta p + \\alpha \\nabla \\cdot \\mathbf{u}) - \\nabla \\cdot K \\nabla p = f$$\n",
    "with boundary conditions on $\\partial \\Omega_d$ and $\\partial \\Omega_n$:\n",
    "$$ p = p_b \\qquad \\quad \\qquad - K \\nabla p \\cdot \\mathbf{n} = v_b$$\n",
    "$$ \\mathbf{u} = \\mathbf{u}_b \\qquad \\frac{1}{2}D(\\nabla \\mathbf{u} + \\nabla \\mathbf{u}^T) \\cdot \\mathbf{n} = t_b$$\n",
    "\n",
    "In the above, the unknowns are the displacements $\\mathbf{u}$ and the pressure $p$. The parameters are the scalar and vector source/sink terms $F$ and $f$, the permeability matrix $K$, the stiffness matrix $D$, the Biot coefficient $\\alpha$, the fluid compressibility and density $\\beta$ and $\\rho$ and the gravity vector $\\mathbf{g}$. $p_b$ is the pressure at the boundary (Dirichlet condition), $v_p$ is the flux at the boundary (Neumann condition), $\\mathbf{u}_b$ is the displacement at the boundary (Dirichlet condition) and $t_b$ is the traction at the boundary (Neumann condition).<br>\n",
    "\n",
    "We present step-by-step how to create the grid, declare the problem data, assemble the system of equations and finally solve the problem.\n",
    "We start by importing some modules."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "ename": "ModuleNotFoundError",
     "evalue": "No module named 'p'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-10-e9cb72bf93da>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mporepy\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mpp\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m \u001b[0;31m# Also import some classes that are convenient for discretization of time dependent problems\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 7\u001b[0;31m \u001b[0;32mfrom\u001b[0m \u001b[0mp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mutils\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mderived_discretizations\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mimplicit_euler\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mIE_discretizations\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'p'"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import scipy.sparse as sps\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import porepy as pp\n",
    "# Also import some classes that are convenient for discretization of time dependent problems\n",
    "from porepy.utils.derived_discretizations import implicit_euler as IE_discretizations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_grid(nx=[4, 4]):\n",
    "    # Define a grid for a toy problem\n",
    "    gb = pp.meshing.cart_grid([], nx)\n",
    "    gb.compute_geometry()\n",
    "    gb.assign_node_ordering()\n",
    "    return gb"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Methods to assign data and initial conditions. We will mainly use default values for parameters, while overriding some of the values. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def assign_data(g, d, parameter_keyword_flow, parameter_keyword_mechanics):\n",
    "    \n",
    "    # Assign a non-default permeability and compressibility, for illustrative purposes\n",
    "    k = 2 * np.ones(g.num_cells)\n",
    "    perm = pp.SecondOrderTensor(k)\n",
    "    fluid_compressibility = 0.1 * np.ones(g.num_cells)\n",
    "    \n",
    "    bound_faces = g.get_all_boundary_faces()\n",
    "    bound_flow = pp.BoundaryCondition(\n",
    "        g, bound_faces.ravel(\"F\"), [\"dir\"] * bound_faces.size\n",
    "    )\n",
    "    bound_mech = pp.BoundaryConditionVectorial(\n",
    "        g, bound_faces.ravel(\"F\"), [\"dir\"] * bound_faces.size\n",
    "    )\n",
    "    boundary_values_flow = np.zeros(g.num_faces)\n",
    "    boundary_values_flow[0] = 1\n",
    "    \n",
    "    \n",
    "    # Create a dictionary to override the default parameters\n",
    "    specified_parameters_flow = {\"second_order_tensor\": perm, \"biot_alpha\": 1,\n",
    "                                 \"bc\": bound_flow, \"bc_values\": boundary_values_flow,\n",
    "                                \"time_step\": 0.3, \"mass_weight\": fluid_compressibility}\n",
    "    specified_parameters_mechanics = {\"biot_alpha\": 1, \"bc\": bound_mech}\n",
    "    \n",
    "    # Initialize the parameters for flow and transport.\n",
    "    # The following keywords are used to define which set of default parameters to pick, i.e. the\n",
    "    # type of parameters. For example, initialize_default_data initializes a second order permeability\n",
    "    # tensor in the flow data, and a fourth order stiffness tensor in the mechanics data.\n",
    "    parameter_type_flow = \"flow\"\n",
    "    parameter_type_mechanics = \"mechanics\"\n",
    "    pp.initialize_default_data(g, d, parameter_type_flow, specified_parameters_flow,\n",
    "                               parameter_keyword_flow)\n",
    "    pp.initialize_default_data(g, d, parameter_type_mechanics, specified_parameters_mechanics,\n",
    "                               parameter_keyword_mechanics)\n",
    "    pp.set_state(d, {parameter_keyword_mechanics: {'bc_values': np.zeros(g.dim * g.num_faces)}})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def initial_condition(g, d, kw_m, kw_f, variable_m, variable_f):\n",
    "    d_0 = np.zeros((g.dim, g.num_cells))\n",
    "    d_0[0,:] = 1\n",
    "    d_0 = d_0.ravel('F')\n",
    "    p_0 = np.ones(g.num_cells)\n",
    "    p_0[-1] = 2\n",
    "    state = {variable_m: d_0, variable_f: p_0}\n",
    "    pp.set_state(d, state)\n",
    "    return d_0, p_0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem setup\n",
    "The practical way of setting up a problem on a single grid with two variables and multiple terms is described here. First, we define a grid and assign data, which we tag with a keyword. The purpose of this keyword is for the discretization operators (such as `pp.Mpsa()` below) to identify which parameters to use. For more details and explanations, see the tutorial on parameter assignment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define a grid\n",
    "gb = make_grid()\n",
    "g = gb.grids_of_dimension(2)[0]\n",
    "data = gb.node_props(g)\n",
    "# Assign data, tagging them with the following keywords\n",
    "kw_f = \"flow\"\n",
    "kw_m = \"mechanics\"\n",
    "variable_f = \"pressure\"\n",
    "variable_m = \"displacement\"\n",
    "assign_data(g, data, kw_f, kw_m)\n",
    "d_0, p_0 = initial_condition(g, data, kw_m, kw_f, variable_m, variable_f)\n",
    "data[pp.STATE][variable_m] = d_0\n",
    "data[pp.STATE][variable_f] = p_0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, discretize the mechanics related terms using the Biot class. This is a dirty trick to ensure efficient discretization where we re-use the local gradient systems of MPSA (see pp/numerics/fv/mpsa.py) for all the mechanical terms involved."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "biot_discretizer = pp.Biot(kw_m, kw_f, variable_m, variable_f)\n",
    "biot_discretizer._discretize_mech(g, data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Assembly\n",
    "The equations we assemble are a *discretized* version of the Biot equations. This requires a spatial discretization of the individual terms, taken care of by objects such as e.g. `pp.Mpsa` for the $\\nabla \\cdot \\frac{1}{2}D(\\nabla \\mathbf{u} + \\nabla \\mathbf{u}^T)$ term, see below. However, a *temporal* discretization must also be chosen, with some implications on the assembly. In this case, we use the Implicit Euler, and therefore need to change the standard PorePy discretization objects for the mass term $\\frac{\\partial}{\\partial t}\\beta p$ and the flow term $\\nabla \\cdot K \\nabla p$, so that hte former returns a term to the right hand side, whereas the latter must be multiplied by the time step. Classes that make this modifications (essentially wrappers around standard discretizations) are available by the imported IE_disrcetization.\n",
    "\n",
    "The assembly requires some information about the relationship between variables, terms (of the equation) and discretization objects to be stored in the data dictionary `d`. The information includes the names of the primary variables and identification of the terms of the equations and which objects to discretize them with. Note that the numbering of the terms (i and j in \"term_ij\") corresponds to the Biot equation as defined above, since stress equals stiffness tensor times the symmetric gradient of displacement."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Variable names\n",
    "v_0 = variable_m\n",
    "v_1 = variable_f\n",
    "# Names of the five terms of the equation + additional stabilization term.\n",
    "#                                        Term in the Biot equation:\n",
    "term_00 = \"stress_divergence\"          # div symmetric grad u\n",
    "term_01 = \"pressure_gradient\"          # alpha grad p\n",
    "term_10 = \"displacement_divergence\"    # d/dt alpha div u\n",
    "term_11_0 = \"fluid_mass\"               # d/dt beta p\n",
    "term_11_1 = \"fluid_flux\"               # div (rho g - K grad p)\n",
    "term_11_2 = \"stabilization\"            #\n",
    "\n",
    "# Store in the data dictionary d and specify discretization objects.\n",
    "data[pp.PRIMARY_VARIABLES] = {v_0: {\"cells\": g.dim}, v_1: {\"cells\": 1}}\n",
    "data[pp.DISCRETIZATION] = {\n",
    "    v_0: {term_00: pp.Mpsa(kw_m)},\n",
    "    v_1: {\n",
    "        term_11_0: IE_discretizations.ImplicitMassMatrix(kw_f, variable_f),\n",
    "        term_11_1: IE_discretizations.ImplicitMpfa(kw_f),\n",
    "        term_11_2: pp.BiotStabilization(kw_f, v_1),\n",
    "    },\n",
    "    v_0 + \"_\" + v_1: {term_01: pp.GradP(kw_m)},\n",
    "    v_1 + \"_\" + v_0: {term_10: pp.DivU(kw_m, kw_f, v_0)},\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Assembly of the global linear system can in many cases be carried out by a single function call of the assembler. Note that for the current problem, this is not possible. Rather, we had to discretize first by calling `biot_discretizer._discretize_mech(g, d)`.\n",
    "Below, A is the global linear system and b is the corresponding right hand side. We obtain the displacement and pressure solution by solving the linear system. We solve the transient system for three time steps, updating the solution vectors in the data dictionary for each step, and also storing all solutions for examination."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "assembler = pp.Assembler(gb)\n",
    "# Discretize the flow and accumulation terms - the other are already handled by the biot_discretizer\n",
    "assembler.discretize(term_filter=[term_11_0, term_11_1])\n",
    "\n",
    "time_steps = np.arange(3)\n",
    "stored_pressures = []\n",
    "stored_displacements = []\n",
    "for _ in time_steps:\n",
    "    A, b = assembler.assemble_matrix_rhs()\n",
    "    x = sps.linalg.spsolve(A, b)\n",
    "    # Distribute the variables (pressure and displacement) on the data\n",
    "    # dictionaries of the grid bucket\n",
    "    assembler.distribute_variable(x)\n",
    "    displacement = data[pp.STATE][variable_m]\n",
    "    pressure = data[pp.STATE][variable_f]\n",
    "    pp.set_state(data, {variable_m: displacement, variable_f: pressure})\n",
    "    stored_pressures.append(pressure)\n",
    "    stored_displacements.append(displacement)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualization\n",
    "We visualize the initial condition and the final solution cell-wise using PorePy's plotting functionality, representing the pressure by colors and displacement by arrows. To plot the displacement vectors, we first need to reshape them and add a zero value for the z direction. We also scale the values using the `vector_scale` argument for visualization purposes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/eke001/anaconda3/envs/pp/lib/python3.6/site-packages/mpl_toolkits/mplot3d/axes3d.py:753: UserWarning: Attempting to set identical bottom==top results\n",
      "in singular transformations; automatically expanding.\n",
      "bottom=0.0, top=0.0\n",
      "  'bottom=%s, top=%s') % (bottom, top))\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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yMr744gt8Ph9jx46lpKSEL7/8kvr6egoKCpgxY0aLOmbMmMFzzz2HtZY1a9bQo0cP+vbte8xzd6Tu3bt3N/2CLioqIhAI0KtXry6/787G3BGdjdlayw033EB2djZ33nlnSOPuSN2djfvrr7+msrISCP5Yeueddxg2bFhI4u5I3Z2J+7HHHqOsrIzt27dTUFDAd7/7Xf74xz+GJGaJIAcltxgMqfvzeDwkJydTXV3Nvn37AJpacQMHDmTBggVMnToVv9/P9ddfz4gRI1i8eDEA+fn55OXlUVhYSFZWFsnJySxZsqTD5z1W3a+++iqLFi3C4/GQlJREQUFBh7qGZs+ezYoVK6ioqCAzM5OHHnoIr9fb5Zg7UndnY165ciXPP/88I0eOJCcnuMTwo48+yldffdXluDtSd2fj3rVrF9deey1+v59AIMCVV17JJZdcEpJ/Ix2pu7NxtyUUMUuENA4ocQgtVhpiNTU1rFmzBgj+une73dTV1REXFwcEu2YGDBiAx+Np9YUxbdq0Vl1EoaK6nVF3d4w53HWfYMK3WOmpxhZfc+xyR2N+F1uLlapbMoyMMeTm5uL1eqmrqwOCLTifz8e2bdtaXWAPxbWvo1Hdzqi7O8Yc7rpF2qJuyTBr7KKsqamhpqaGpKQkjDGMHHkmNTWHWpUP5+ix0NbtAXxhqrul8NXt7pZxf1uvG/CHqe7QO7LutLQeHDxYGbbzyXHSYqXSGUlJSdTV1TUNNAkmtsJoh9UFecDb0Q6ii6YA3fm6z0+A30U7iE47dOjn0Q5BjuSga25KbhGUkJCA1+uluLg42qGIiLTksJabrrlFWFxcHEOGDIl2GCIijqbkFgWhuK9MxAlyc3OZNm1atMMQ0E3cIiKhUlxc3OIWAS2ZE0VKbiIi4fHEE0+QnZ3d5r4333yTkpISSkpKeOqpp7j55psjHN0JIIyrAkSakpuIxAQtmRNlarmJiISelsyRUFJyE5Go05I5McBhLbcYDElETjSNS+YUFhZSW1vLwYMHueaaa1qsLKAlcyIgBq+ddZZabiISdVoyJwao5SYiEhlaMieCHDZDiYPeiog4wYUXXsiFF14IBJNaI2MMCxcujFJU0t0ouYmIiOMWK1VyExERdUuKiIhDOSgjaLRkiNXX10c7BBGRE56D8nRs2Lt3L1VVVSQlJR11pgURkZjjsG5JffuGWGZmJomJiVRXV1NXV0cgEIhSJE8AviidOxS+Bm4C7ol2IF1ggb0Nf4rEuMYBJZo4WY7G7XaTmpoKQFFREX6/P8IRrAT+CtRE+Lyh8g/gGmA7MCy6oXSKF/gV8H+Au4HS9ouLxAKH3cSt5BZGCQkJDB8+nNraWurq6iJ01t3AfxD8l/pxhM4ZaqOBLIItnslRjqUzPEAawZbz+cDp0Q3nuHwC3AfcBfw8yrFIxCm5SUelp6eTkpICQFVVVQRacT5gJMEv171hPle4pBPsVv0VcFqUY+kMQ7BL9V+AH0Y5luN1GsGWpwHyj1FWJHbFYL51poSEBOLi4qipqaGkpCSMZ8oEfhPG+iPFA0yMdhBd0IPueb2wB/A9IAAMiXIsElG6iVs6y+VykZKSgsejj11i2UXRDkCiQaMlpasGDhwY7RBEYkJubi7Tpk2LdhgCGlAiIhIqxcXFLF++HIDa2lrGjRvH6NGjGTFiBA888ECr8itWrKBHjx7k5OSQk5PDww8/HOmQnc1BtwLEYL4VkRNRQkIC7777LqmpqXi9Xs477zymT5/OhAkTWpSbOHEiy5Yti1KU0l2o5SYiMcEY03R/qNfrxev1YoyJclQnkAh0SxpjphljPjfGbDXGtBpxZYy52hjzUcO2yhgzutm+7caYj40xG40xxcc6l5KbiMQMv99PTk4Offr0YcqUKYwfP75VmdWrVzN69GimT5/O5s2boxClQ4U5uRlj3MBCYDowHJhtjBl+RLEvgQustaOAXwNPHbF/krU2x1qbe6zzKbmJSMxwu91s3LiRsrIyioqK2LRpU4v9Y8aMYceOHXz44Yf89Kc/ZebMmVGK1IHC33IbB2y11m6z1tYDBcBlzQtYa1dZaw80PF1D8N6mTlFyE5GYk5GRwYUXXtg02KRRenp6U9dlXl4eXq+XioqKaIQox+80Ws5FV0b7szTcALzZ7LkF/mqMWW+MuelYJ1NyE5GY8PXXX1NZWQlATU0N77zzDsOGtZxbdPfu3VgbnIi6qKiIQCBAr169Ih6rY3VttGRvY0xxs+3IBNTWBdQ2ZxU3xkwimNzubvbyudbaMQS7NW81xpzf3lvRaEkRiQm7du3i2muvxe/3EwgEuPLKK7nkkktYvHgxAPn5+bz66qssWrQIj8dDUlISBQUFGnQSKl2/ibviGNfCyoD+zZ5nAjtbhWHMKOBpYLq1dl/j69banQ1/7jXGvEawm/PvRzuZkpuIxIRRo0axYcOGVq/n5387x+W8efOYN29eJMM6cYR/hpJ1wBBjzECgHJgFXNUiBGNOB/4E/Nhau6XZ6ymAy1p7qOHx94B2b3JUchMRkaAw3oxtrfUZY+YBbzWc6Rlr7WZjTH7D/sUEZ0vvBfy+oUXua2gNngK81vCaB3jRWru8jdM0UXITEZGIsNYWAoVHvLa42eO5wNw2jttGcC2sDlNyExERx02c7KC3IiIinabkJiIijqPkJu1pvAdHRKS7sTE4u39n6SbuECstLaW6uhqfzxftUERETlhquYXY6aefTmlpKfX19dTV1VFWVoa1VjeaikhMswb8DsoIDnorscPtdpOUlIS1ltraWqqqqoiLiyM+Pl5JTkRik5KbdJQxhqysLPbu3YvX66W6uhqXy8XBgwcJ3sOYF+0Qu8ANTIl2EF3kAn4S7SC6wAX8PNpBdIGDLvA4gDXgc3flSlUgZLGEgpJbhMTFxREXF4fP52Pr1q2AH0w3HnxiDXi6cfwAPgO8F+0oumAS8GC0g+iCB6MdgDiYkluEeTwexowZE+0wRGJCbm4uvXv3brW0jUSeNQa/pyspoT5ksYSCkpuIRE1xcXHT49raWs4//3zq6urw+Xz84Ac/4KGHHmpR3lrL7bffTmFhIcnJyTz77LP6sRhCfrdzuoqV3EQkJiQkJPDuu++SmpqK1+vlvPPOY/r06UyYMKGpzJtvvklJSQklJSWsXbuWm2++mbVr10YxauewGPwOug6q5CYiMcEY07TKttfrxev1thpdvHTpUubMmYMxhgkTJlBZWcmuXbvo27dvNEJ2FIvB56Dkppu4RSRm+P1+cnJy6NOnD1OmTGH8+PEt9peXl9O//7frXWZmZlJeXh7pMKUbUHITkZjhdrvZuHEjZWVlFBUVsWnTphb725reTveOho4fT6e3WKPkJiIxJyMjgwsvvLDVKMrMzExKS0ubnpeVldGvX79Ih+dIjdfcOrvFGiU3EYkJX3/9NZWVlQDU1NTwzjvvMGzYsBZlZsyYwXPPPYe1ljVr1tCjRw9dbwsRpyW32GtLisgJadeuXVx77bX4/X4CgQBXXnkll1xyCYsXBxdqzs/PJy8vj8LCQrKyskhOTmbJkiVRjtpZYjFJdZaSm4jEhFGjRrFhw4ZWr+fn5zc9NsawcOHCSIYl3ZSSm4iIOO5WACU3ERFpuObmnJTgnHciIiJd4qRrbhotKSIijqPk5lS2Guz10Y6i66wfAoXgGwq+OdGORsSxnHYrgJKbE9kA8D1gCdhd0Y6ma2wBBC4GtoDJjXY0Io5lAR/uTm+xRtfcHOl5YCVggHXAjOiG0xU2HUgCasB1ZbSj6YR9wFpgC5AOOKA1LQ6lASUS82YBvwdOAU6PcixdYNeCvQFc74LpCebUaEfUCUXAfzY8nhzNQETapSVvpF3l5eXU1NTgdrtxu90EAoHIB2ESwP4PMAxMN/4rtmvB9Ry4Jhy7bEzyE2xFpwEJwC+jG85xeR/4jGDLMwO4JbrhiBynbvzNF5v69u3L9u3b8fv91NfXs2bNGqqqqpqSnTtSK92aMyJznnBy3RbtCLrIDfx/BLuHa4G46IZzXFzA7oY/86Ici0SKk1puGlASYi6XC7fbTXx8PElJSZxzzjkkJyfj8XgIBALU1NSwcuXKaIcpEdML6Al0t5nrxxNscf4AGBDdUCQinDZaUi23CDDG4PF48Hg8JCQkcPbZZ0c7JJFjiAfuINy/f3Nzc+ndu3erpW0k8pw2/ZZablGgxRWlewj/10NxcXFTYistLWXSpElkZ2czYsQInnjiiVblV6xYQY8ePcjJySEnJ4eHH3447DFK96SWm4jEBI/Hw+9+9zvGjBnDoUOHOOuss5gyZQrDhw9vUW7ixIksW7YsSlE6m24FEBEJsb59+zYtPJqWlkZ2djbl5eWtkpuEh9NuBVC3pIjEnO3bt7NhwwbGjx/fat/q1asZPXo006dPZ/PmzVGIzpmcNqBEyU1EYsrhw4e54oorePzxx0lPT2+xb8yYMezYsYMPP/yQn/70p8ycOTNKUTpTuKffMsZMM8Z8bozZaoy5p439VxtjPmrYVhljRnf02CMpuYlIzPB6vVxxxRVcffXVXH755a32p6enk5qaCkBeXh5er5eKiopIhymdYIxxAwuB6cBwYLYx5sg+5y+BC6y1o4BfA08dx7EtKLmJSEyw1nLDDTeQnZ3NnXfe2WaZ3bt3Y60FoKioiEAgQK9evSIZpmM1Llba2a0DxgFbrbXbrLX1QAFwWYsYrF1lrT3Q8HQNkNnRY4+kASUiEhNWrlzJ888/z8iRI8nJyQHg0Ucf5auvvgIgPz+fV199lUWLFuHxeEhKSqKgoEC31oRICAaU9DbGFDd7/pS19qlmz08DSps9LyM4W8DR3AC82cljldxEJDacd955Ta2yo5k3bx7z5s2LUEQnni4mtwprbXvrUrX1K6TNv3BjzCSCye284z22kZKbiIhEYoaSMqB/s+eZwM4jCxljRgFPA9OttfuO59jmdM1NREQiYR0wxBgz0BgTT3BtrtebFzDGnA78CfixtXbL8Rx7JLXcRESkaUBJ2Oq31meMmQe8RXDJjGestZuNMfkN+xcDvyI42/jvG66l+qy1uUc7tr3zKbmJiAgQ/iVvrLWFQOERry1u9nguMLejx7ZHyU1ERDT9loiISKxTy01ERBzXclNyExERAC1WKiISq+6///4WC53ee++9/Pd//3cUI+oeIjD9VkQpuYmIo9xwww384Q9/ACAQCFBQUMDVV18d5ahin9OWvIm9dCsi0gUDBgygV69ebNiwgT179nDmmWdqcuUTkJJbGNTX11NfXw/AqlWrOHz4cIv9q1atAuLAducJXz3g687xQ/Be0EnRDqILXMCD0Q6iC1zk5ubSu3dvli9fTmlpKXPmzGH37t24XC5uuukmbr/99hZHWGu5/fbbKSwsJDk5mWeffZYxY8a0qnnu3Lk8++yz7N69m+uvvz5Sb6jbi8UWWGcpuYVBfHw88fHxAJxzzjkNyexb55xzDuCFpe1PEhvTLjMwuxvHD/CSIbh8VHc1EPhNtIPogvsoLv52EnmPx8Pvfvc7xowZw6FDhzjrrLOYMmUKw4d/u2zXm2++SUlJCSUlJaxdu5abb76ZtWvXtqr5+9//Pr/61a/wer28+OKLEXk33V0E5paMKCU3EYkJffv2pW/fvgCkpaWRnZ1NeXl5i+S2dOlS5syZgzGGCRMmUFlZya5du5qOaxQfH8+kSZPIyMjA7XbOF3Y4hXv6rUhzzjsREcfYvn07GzZsYPz4lkt2lZeX07//t5PDZ2ZmUl5e3iq5BQIB1qxZwyuvvBKReJ3CSd2SGi0pIjHl8OHDXHHFFTz++OOkp6e32NfWem9HLlb6ySefkJWVxUUXXcSQIUPCGqvELrXcRCRmeL1errjiCq6++mouv/zyVvszMzMpLf12QeaysjL69evXoszw4cPZtm1b2GN1GqfNUKKWm4jEBGstN9xwA9nZ2dx5551tlpkxYwbPPfcc1lrWrFlDjx49WnVJSufpPjcRkRBbuXIlzz//PCNHjiQnJweARx99lK+++gqA/Px88vLyKCwsJCsri+TkZJYsWRLNkB1FoyVFRMLgvPPOa/OaWnPGGBYuXBihiKQ7U3ITERHdCiDd1J7tcMqAaEchIjHKf4mQAAAgAElEQVQsFq+ddZYGlDidtfDC/XDTQDhcGe1oRCRGaeJk6V7+8gS8/BswBg7tg9SMaEckIjHIaQNK1HJzurGXQEIyxCVCwB/taEREIkLJzem+2gwDRsPLVXDav0Q7mtA4+DlsWQhvnwNlr0c7GhHHcNJipbEXkYRW4e9h+s3Bbkmn+OBO2FUYfJx0SnRjEXEIp81QouTmZLu2wpcb4N6l0Y4kdHa/AweKwZUAp82AXuOPfYyIHJOSm3QfyxfDRddDfGK0I+m6gA82PQjblsDZL0LKdyBBqyuLhJKSm8S+uhp49w/w26JoR9J11WWw6ipwJ8LUD7pxV+TjwEuAH7ga+Fl0wxFxMCU3p1r5CgwZB6cMjHYkXVO+DIrmwtA7IPuXYLrjGKgA8E/gbWAv4AbOiWpEIkdy2q0ASm4RFggE2L17d/hPNCgHhowN/3nCadfbUHwrnPe/cPK50Y6mk14GFgHJwCxgCfBrIJavFe4HDJAG7AF6AwlRjUjCT9NvSYdZazlw4AD19fX4fD4CgQDGGA4dOhT+kw8YFf5zhFufC+Diz8CTFO1IuqAW+C0whmDC+HF0w+mQPwJfAxY4CZgDnByWM+Xm5tK7d2+WL1/O9ddfz7Jly+jTpw+bNm1qVXbFihVcdtllDBwY7I24/PLL+dWvfhWWuE5UuuYmR/XNN99QW1uL3+/HWkt5eTkAiYmJuFzBLjWtDtxB7vhoRxACc6IdQCeMAN4DRgOXQxi/8IqLi5seX3fddcybN485c47+mU2cOJFly5aFLR5xDiW3EHO5XHg8HhISEjDGcMYZZ7Bq1apohyVyHMYRbGVeSCTneTj//PPZvn17xM4nLTntVoDueHU+pqWlpeHxeDBOumlaTjBpwHeJxa+H1atXM3r0aKZPn87mzZujHY6jNA4o6ewWa9RyE5FuYcyYMezYsYPU1FQKCwuZOXMmJSUl0Q7LUZw0oCT2fpqJiLQhPT2d1NRUAPLy8vB6vVRUVEQ5Kudw2pI3Sm4i0i3s3r0bay0ARUVFBAIBevXSLDXdiTFmmjHmc2PMVmPMPW3sH2aMWW2MqTPG/OKIfduNMR8bYzYaY4qPPPZIzmmDiki3Nnv2bFasWEFFRQWZmZk89NBDeL1eAPLz83n11VdZtGgRHo+HpKQkCgoKdG07hMI9oMQY4wYWAlOAMmCdMeZ1a+0nzYrtB24DZh6lmknW2g4115XcRCQmvPTSS+3unzdvHvPmzYtQNCemMA8MGQdstdZuAzDGFACXAU3JzVq7F9hrjLm4qydTchMRkVDMUNL7iO7Cp6y1TzV7fhpQ2ux5Gcc3VY8F/mqMscCTR9TdipKbiIiEoluywlqb287+tvqQ7XHUf661dqcxpg/wtjHmM2vt349WWANKREQkEsqA/s2eZwI7O3qwtXZnw597gdcIdnMelZKbiIgAhPtWgHXAEGPMQGNMPMGZxF/vyIHGmBRjTFrjY+B7QOsJSJtRt6SIiIR9tKS11meMmQe8RXDC0mestZuNMfkN+xcbY04FioF0IGCMuQMYTnBpitcaRsd6gBettcvbO5+Sm4iIYAn7aEmstYVA4RGvLW72eDfB7sojHSQ4k3eHqVtSREQcRy03EREBLVYqIiJO47Qlb5TcREQE0ErcIiLiMI3ruTmFBpREQV1dXbRDEBFxNCW3CPL7/dTU1PDBBx9EOxSRmJCbm8u0adMAuP766+nTpw9nnHFGm2Wttdx2221kZWUxatQo/T8Ksca5JTu7xRoltzCz1uL1eqmqqqKuro64uDgmTJgQ7bBEYkJxcTHLlwfvxb3uuuuaHrflzTffpKSkhJKSEp566iluvvnmSIV5wnDSYqWxl24dojGprVq1Cr/fT1JSEi5X8LeEMQbcHrisG69FZTzwUjeOHwj+8x8Y7SC6wAXcF+0guqDlF+L555/P9u3bj1p66dKlzJkzB2MMEyZMoLKykl27dtG3b98wx3li0GhJaVd1dTW1tbX4fD7i4+MZN24c69ata13Q7+PBiEcXOg9aHyw8ngm9Y9CtBtgS7Si64F+A30c7iC645bhKl5eX07//t/PuZmZmUl5eruQWIhaDP6DkJkdRVVWF2+0mMTERgLi4uChHJOIM1rb+MaWVuOVolNxC7OSTT+aLL76IdhgijpOZmUlp6bdrXZaVldGvX78oRuQwFnw+57TcNKBERLqFGTNm8Nxzz2GtZc2aNfTo0UNdkiFkrcHv83R6izWxF5GInJBmz57NihUrqKioIDMzk4ceegiv1wtAfn4+eXl5FBYWkpWVRXJyMkuWLIlyxM4STG7OabkpuYlITHjppZfa3W+MYeHChRGKRro7JTcREQGLWm4iIuIs1hp8XiU3ERFxFEPA75yU4Jx3IiIinWcBB3VL6lYAERFxHLXcREQErHFUy03JTUREGrolnTOdmZKbiIgE+aIdQOgouZ0gAsDHwAfAPuAX0Q1HRCSslNxOEDXA64AfyIxyLCISgyxquUn3YoENQDxQC3wvuuGE1oEy+OwdOP0sODU7uAisiBw/JTfpqkAgELFz+YFCoAzIJ7j2cWrEzh5mdVWw8il48zeAhZOHwIPdefFRkSiygDfaQYSO7nOLML/fz9q1ayNyrlrgReAb4CdAD7p5Ygv44cu1sPwRePxCuOeUYKsNoOd34Pb3ohpe++px1DdHiOTm5jJt2jQAli9fztChQ8nKymL+/Pmtyq5YsYIePXqQk5NDTk4ODz/8cKTDdTZL8NdwZ7cYo5ZbBNXV1eHz+Tj77LMjcr5CIAPII9hi65YqtsEnb8Fnb8OW9+CkTBg6GSbfBVkXQGIqfPjn4GuJsZq6LfAg8BdgFHAXkBPNgDqgGEgCsgnnb+Di4mIg+KPv1ltv5e233yYzM5OxY8cyY8YMhg8f3qL8xIkTWbZsWdjiEedQcosAv99PbW0tHo+HlJQUUlMj8yU8g27+F+z3wtM/gH4jIedy+NFC6NHG4pSjZ0Y+tg77DfC/BFtt9cB64DNiP7m9DZQDBpgIXBnWsxUVFZGVlcWgQYMAmDVrFkuXLm2V3CTMdM1NOsJay+eff05tbS1JSUm4XJHtBe72f7nuOLjng2hH0UXzgJ8CW4D/H3gYODWqEXVMOsErtWcB54X9bOXl5fTv37/peWZmZpvd96tXr2b06NH069eP3/72t4wYMSLssZ0wNKBEOsLv91NTU0NmZiYpKSnRDkeiJqPhz7ENW3dxGXA50EZLOQysta1eM6blbBljxoxhx44dpKamUlhYyMyZMykpKYlIfCcEhyU3DSgJMZ/PR21tLbW1tSQnJ/Od73wn2iGJdEImkUpsEGyplZaWNj0vKyujX79+Lcqkp6c3denn5eXh9XqpqKiIWIyO15jcOrvFGCW3ENu5cycul4uUlJSId0OKdFdjx46lpKSEL7/8kvr6egoKCpgxY0aLMrt3725q4RUVFREIBOjVq1c0wpVuQN++IXb66acTHx8f7TBEuhWPx8OCBQuYOnUq2dnZXHnllYwYMYLFixezePFiAF599VXOOOMMRo8ezW233UZBQUGrrkvpggi03Iwx04wxnxtjthpj7mlj/zBjzGpjTJ0x5hfHc+yRdM1NRGJCXl4eeXl5LV7Lz89vejxv3jzmzZsX6bBOLGHsXjTGuIGFwBSCo5XWGWNet9Z+0qzYfuA2YGYnjm1BLTcREfl2hpLObsc2Dthqrd1mra0HCgiOXPo2BGv3WmvXtVHjMY89kpKbiIhEwmlAabPnZQ2vheVYdUuKiMi30291Xm9jTHGz509Za59q9rytC6St7wFp23Efq+QmIiKhuM+twlqb287+MqB/s+eZwM4O1n3cx6pbUkREIjFach0wxBgz0BgTD8wiuMxkWI5Vy01ERMI+Q4m11meMmQe8RXAu92estZuNMfkN+xcbY04lOGt3OhAwxtwBDLfWHmzr2PbOp+QmIiIRYa0tJLhgSfPXFjd7vJtgl2OHjm2PkpuIiATF4DRanaXkJiIijps4WclNRESU3ERExIEaZyhxCN0KEAVtrV0lIiKho+QWBZs3tzuCVeSEkZuby7Rp0wBYvnw5Q4cOJSsri/nz57cqa63ltttuIysri1GjRvHBB919lfYY0zhDSWe3GKNuyQiy1lJTU8Opp54a7VBEYkJxcXC2Jr/fz6233srbb79NZmYmY8eOZcaMGQwfPryp7JtvvklJSQklJSWsXbuWm2++mbVr10YrdGdy0DU3tdwixFpLdXU1cXFxDBo0KNrhiMSUoqIisrKyGDRoEPHx8cyaNYulS5e2KLN06VLmzJmDMYYJEyZQWVnJrl27ohSxA2klbjlegUCAqqoqEhISiIuLi3Y4IjGjsVuyvLyc/v2/nTowMzOT8vLyFmU7Ukakkbolw2z//v1UV1eTnJyMyxX8LeH3+0lNTubB6uooR9cFbg/c2t1XQfYA/xLtILrADdwS7SC6wM2BAwcAuPvuu6mrq2ux98hVttsaiKWVuENItwJIR3m9XrZs2dIisblcLtasWcPSv/wFn89HXV0dycnJYflPWlNTg8fjCUtrsbGbNVyx19fXAxAfHx/yuhtVVVWRkpIS8np9Ph8+n4/ExMSQ1w1QXV1NQkICbrc75HX7fD7q6+tJSkoK+d+rtZba2lrcbjfx8fHcfffd7N27l3379pGQkEBFRQXTpk1j+fLllJWV0a9fvxbHZ2ZmUlr67ZJebZWRLnDYrQBKbmFSV1eH3+/n3HPPpaioCAj+5x4zZgwAe/bsoaysjNzc3LAkn7KyMg4fPsywYcNCXjfA1q1b6d+/P3379g1L/Zs2bWLAgAGkpqaGpX6AdevWMXbs2JDX6/f7+eCDD8JSN8DBgwfZvn07o0aNCkv9paWlVFdXM3To0JDXHQgE+OSTT0hJSeFvf/sbtbW13HDDDZx55pk8//zzLFq0iPr6egoKCnjxxRdbHDtjxgwWLFjArFmzWLt2LT169Ajbv78TUtfXc4spSm4hFggEqKmpASA5ORmPJ/gRW2txu92sW7cOr9eL1+slKSmJjRs3hjwGv99PXV0dSUlJrFu3LuT1N77HlJQUysrKQl4/BFtVjZ9juFRVVYXl84Fg62rt2rVNLfZQq6mpYc2aNWFpvTXWv2/fvrBdIz5w4ADl5eU88MADfPPNN6xfv57q6mqys7NxuVzce++9jBgxgsWLg3Pq5ufnk5eXR2FhIVlZWSQnJ7NkyZKwxHZCU7ekHM2XX36Jy+UiISGh6bXGxOb3+6mvr8fn84Wl2weCiae2tjZs9UOwyzCc3YV+vz9sSSFSGv++w/U+4uPjm7q0wyExMZHq6mpcLldYEmhiYiK1tbU8+OCDJCYmcvfdd7Nr1y5cLhcDBw7kH//4BxBMao2MMSxcuDDksYgzde9vkBg0cODAFonN6/U2fdE1dlWGK/E0XtNISEgI25dqIBAgEAiEddSn3+9vavF2Vx6PB58vfD+D3W43xpiwncMYQ1JSErW1tWGbUScxMRFjDDU1NcyfP59+/fqRlpZGSUkJe/fubXGDt0SAbgWQ9jRPKi6Xi6KioqbEFggEmv5Dh0NdXR0ejyesiaGuri6srTYIDmoIV3dbpLjdbgKBQFjPkZCQ0GqEYSg19kCEs3u48YdYbW0tjz32GKeccgonn3wyZWVl+Hy+pkEmEgGNA0o6u8UYJbcwcblc+P3Bq7ONv37D2VXo9Xqx1oa9u9BaG9bkaa3FWtvtuyUh+G8gnAmuscvQ6w3fN4vH48Htdoc1iTaO/KypqeGxxx6jV69epKenU15eTn19vRJcpGj6LWmP3+9v0V3UmOASEhLCOmFy49DzcJ7D7/cTHx8f1nM0Js9ITS4dzvN4PB4CgUBY78WKj4+nvr4+rD844uPjqa2tDet7aezm9nq9PPbYYwDcddddfPXVV5x++ulUVFSQm5tL7969Wb58eVhiOOHpPjdpT3JyMhMnTox2GNIBO3bs4Dvf+U60w5CjWLduHd988w09e/aMdijSDSm5hZgTutNOFJrjM/YpsUWYg1pu+iYWkbDbv38/U6ZMYciQIUyZMqVp2q0jHW3Zm6Mdv2/fPiZNmkRqairz5s1rUdf69esZOXIkWVlZ3HbbbU1d0HV1dfzoRz8iKyuL8ePHs3379vC86e5GA0pERI7P/PnzOfvssxkwYAAbNmzgzDPPbJXgGpe9ueeee3C5XDzwwAP87Gc/a/f4xMREfv3rXzN58mSef/55hg4dyltvvQXATTfdRF1dHampqTz77LNkZGRwxx138D//8z/s3buXb775hj179nDmmWfy9NNPR/wziTkOG1Ci5CYiYbd06VIqKiq46KKL+Pjjj6mqqmq1IGlRURGDBw/mN7/5DcuXL+e+++6joKCATz755KjHp6Sk0LNnTz744AOuuuoqli9fzi233EJZWRlVVVVs2bKFjRs38uSTTxIfH8/ll1/O0qVLOffcc/nRj37E1q1bcbvd3HDDDVH6ZCRclNxEJOz27NnD3/72N6699loSEhI4cOAA//Vf/9Wii7G8vJyEhISmdd0OHjxIZWUlEydOZMeOHUc9vqCggHHjxuF2uykoKGDXrl3k5uaSlJTUdP5f//rX7Nu3j9tuu42///3vTaMz/X4/tbW1DBo0SF2UuolbRKS1yZMnc8YZZ7TaGhcd3bNnD3379mX+/PlNt3s072JsXGmif//++P1+nnvuOQYOHNg0CcL27dvbPP7xxx8nJSWF/fv3U1BQQHZ2NnV1dXz44YcUFhYCwWt2jbc0WGt5//33+d///V8GDRpETU2NuihByU1EpC3vvPMOp556aqvX7733XlJSUpoGdDz//PN4vV78fj833XRTUxdjZmYmFRUVWGuZNWsWBw4c4LPPPuPcc8+lV69eeL1ennzySR5//PGmG9c//vhjvF4vxcXFFBYWsmPHDj766CPuu+8+EhISuPHGG3nkkUfYs2cPAE888QQTJ05k79693HXXXRw8eJBAIEB9fT0lJSUndhelwwaUmGPcxBqZO2lFxNHuuusunn32WTZs2MDpp59OYmIiPp8PYwzWWgYOHMjmzZs5/fTT6dmzJ263m08//ZRAIIDL5WLs2LGsXbuWtLQ0Dh8+3DTH6R133MGiRYsIBAJkZGRgjKGiooI+ffpQX19PamoqNTU1fP3113g8Hvx+P2PHjqW6uprDhw9TXl6OMYb6+noGDRqE3++nuLiY3r17R/sjO5qwzQhg0nMtucWdr+A9s95amxu6iLpG97mJSMhNnjyZ3bt3Nz33+/188803DB06FGstNTU13HjjjWRkZPCf//mf7Nq1C4/Hw5NPPslll11GQkICHo+HhIQEEhMT+eqrr3C5XFRWVgLBWVPGjh1LQUFB09RgFRUVGGNIS0vD5/PRs2dPduzYgbWW7OxsNm/ezIQJE9iwYQMQnJ3G7/czadIk3n//fSorK6mrq2Pnzp2xnNykg9QtKSIhd2QXpdvtZvDgwU3T0UFweP+hQ4cwxnDo0CHmz5/PpZdeSm5u8Md/Y2vK4/Gwc+dO3G43cXFxGGPw+/3k5ORw4MCBpokTjDHExcVxzTXXcODAAb744gvcbjdJSUn86U9/YseOHaxfvx6v19s056cxhh07dnDfffdRX19PdXU1eXl5EZv+LaY47JqbuiVFJGJeeeUVfvGLX7Bnzx62bt3KsGHDiIuL4+DBg3g8Hm655Ra2bNnC/v37KSkp4dRTT2Xnzp0cPHiwaZLowYMHN42wdLvdVFZWUl9fT1xcHL169WLw4MGsW7eO+vp6XC4XaWlpFBcX4/F4GDx4MNZaTj755KauyfT09KblqBITEzl8+DCDBg1i9erV9OnTJ8qfWCvh65ZMzbWM6kK35OrY6pZUy01EIiYzM5O0tDQ8Hg8jRozA7/dTVVXFsGHDuP322/n9739PSkoKtbW13HXXXXzyySdUVlYSFxfHySefjMvlYt++fXg8Hvbv309FRQVDhw4lISEBn8/HRRddxMqVK/F6vcTFxZGWlobX6+W8885j9OjRBAIBpk6dyvr16+nduzf9+/dn7Nix+Hw+/H4/559/PoMHD2by5MmxmNjCy2EDSpTcRCRixo4dy/79+xk5ciSZmZnU1dXhcrm4/PLLsdZijOFPf/oT27Zto3///gwbNgxjDF6vl1mzZmGt5cCBAxhjMMbgcrmoqqoiOzsbay1vvPFGUzeltZYf/vCHVFdXs2fPHg4ePAjAihUrGDZsGOXl5VRWVrJu3ToCgQBut5uioiKuvfZaXnrppVbTdjmeZigREemcxkEjxcXF7Nmzh+985zskJydjreXJJ5/krLPOYu7cuVhruf766yktLWXgwIEMGTKE7373u6SkpABw6NAhPB4PaWlpvPbaa5SVlREfH091dTWBQACPx8PPfvYz7rzzzqY1Dnv16kVBQQE1NTUsWbIEr9dLjx49SExMxOVy0aNHD+Lj43nkkUfIyMhgy5YtlJSUaImdbkrJTUQi6tJLL2Xp0qUkJSWxc+dOBg0axMUXX0xiYiK1tbXExcVxzz33kJOTgzGG8vJyfv7zn7N06VJSUlIYPnw4KSkp1NfX079/f6qqqjjppJOYNm0affr0weVy4fP5uOeee8jIyCAtLQ0IrjDw2GOPkZOTwxtvvEFcXFzT9F2BQICzzz6btWvXctJJJxEIBPjjH//InDlz+POf/xzlTyyCHDSgRMlNRCIuLy+PL7/8kl69epGcnMyOHTvw+XxMnDiRfv360b9/f3Jzc3nppZfo3bs3ycnJbNq0iYyMDHw+H8XFxcTHx+NyudixYwcVFRUMHDiQW265halTp5KQkEBdXR1/+MMfuPLKK0lKSmLhwoWsX7+ejRs3snbtWtxuN6tWreLTTz+lV69enH322ezatQuv18sPf/hDioqKyMzMpLy8PNofV2Q4bLSkkpuIREVjF+Xq1auZN28eAwYM4L333qOmpoZ3330XYwx5eXmMGjWKuXPn8tFHHzFz5kx69OjRdD3u448/bnHsjBkzuPTSS/F4PIwcOZK3336b3r1707t3bz744ANGjRrFqFGj2LJlC1dddVXTenETJkxg4cKFzJw5k8TEREpLSznjjDMAwrqSekyJwIASY8w0Y8znxpitxph72thvjDH/3bD/I2PMmGb7thtjPjbGbDTGHHNYp5KbiERN8y7Kzz77jCuvvJKHH36YAwcOUFpaijGGZcuW8ZOf/ARjDH/84x/5/e9/D0BtbS3PPvtsi2NHjBhBZWUld9xxB6NHj+arr75i5cqVnH766Vx00UVs3ryZyZMn43a7KSwsZODAgUyaNImamhpSU1NJT0/n66+/5rTTTuPGG2+krKyMfv36RflTcgZjjBtYCEwHhgOzjTHDjyg2HRjSsN0ELDpi/yRrbU6Hbjmw1ra3iYiEndfrtQMHDrTbtm2zdXV1dtSoUXbTpk0tyixbtsxOmzbNBgIBu3r1ajt27NgOH3vBBRfYdevWNT3ftGmTHTlypD3nnHPsU089ZQcOHGh9Pp+11trc3Fy7evVqGwgE7LRp0+wbb7wR5nd/XI71nd3pjfizLANt5zcobrd+OBt4q9nzfwX+9YgyTwKzmz3/HOjb8Hg70Luj70ctNxGJOo/Hw4IFC5g6dSrZ2dlNrbDFixezePFiIHidbtCgQWRlZXHjjTc2teCOdizAa6+9RmZmJqtXr+biiy9m6tSpAIwYMYKkpCQ+/fRTfvvb37Jw4ULcbjcAixYtYu7cuWRlZTF48GCmT58ehU8kCrp+za23Maa42XbTEWc4DSht9rys4bWOlrHAX40x69uouxXNUCIiJ5xnn32WV155hb/85S9N98V1E+GboSQ+19K7CzOU7Gp/hhJjzA+BqdbauQ3PfwyMs9b+tFmZN4DHrLX/bHj+N+CX1tr1xph+1tqdxpg+wNvAT621fz/a+TRxsoicUNavX89vf/tb/vGPf3S3xBZejQNKwqcM6N/seSaws6NlrLWNf+41xrwGjAOOmtz0NysiJ5QFCxawf/9+Jk2aRE5ODnPnzo12SCeKdcAQY8xAY0w8MAt4/YgyrwNzGkZNTgC+sdbuMsakGGPSAIwxKcD3gE3tnUwtNxE5oSxZsiTaIcSmxum3wlW9tT5jzDzgLcANPGOt3WyMyW/YvxgoBPKArUA18JOGw08BXmu4LcMDvGitbXfqGF1zExHpPsJ3zc2da0npwjW3Q7G1KoBabiIi8u1oSYdQchMRkUgMKIkoDSgRERHHUctNRESCYnBdts5SchMRkSAHDSFUt6SIiDiOkpuIiDiOkpuIiDiOkpuIiDiOBpSIiAhOu9FNyU1ERHDaFCXqlhQREcdRy01ERFC3pIiIOJCzuiWV3EREBLXcRETEgZyV3DSgREREHEctNxERaaBrbiIi4ijO6pZUchMREZw2WlLX3ERExHHUchMREdQtKSIiDuSsbkklNxERQS03ERFxIGe13DSgREREHEctNxERQd2SIiLiQM7qllRyExERnNZy0zU3ERFxHLXcRESkgbolRUTEUZzVLankJiIiKLmJiIgDOWu0pAaUiIhIRBhjphljPjfGbDXG3NPGfmOM+e+G/R8ZY8Z09NgjqeUmIiKEu1vSGOMGFgJTgDJgnTHmdWvtJ82KTQeGNGzjgUXA+A4e24KSm4iIEIFuyXHAVmvtNgBjTAFwGdA8QV0GPGettcAaY0yGMaYvMKADx7ag5CYiIoSg5dbbGFPc7PlT1tqnmj0/DSht9ryMYOuMY5Q5rYPHtqDkJiIihKDlVmGtzW1nvznKSTtSpiPHtqDkJiIikVAG9G/2PBPY2cEy8R04tgWNlhQREb7tluzsdkzrgCHGmIHGmHhgFvD6EWVeB+Y0jJqcAHxjrd3VwWNbUMtNREQI94ASa63PGDMPeAtwA89YazcbY/Ib9i8GCoE8YCtQDfykvWPbO58JDsLBvC8AAAB/SURBVEo5ejxdfD8iIhI6bV17Ck3F5jQLt3ShhvvWH+OaW0SpW1JERBznWC03ERE5ARhjlgO9u1BFhbV2Wqji6SolNxERcRx1S4qIiOMouYmIiOMouYmIiOMouYmIiOMouYmIiOMouYmIiOMouYmIiOMouYmIiOMouYmIiOP8PzVgZbzYxAczAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "d_0 = np.reshape(d_0, (2, g.num_cells), 'F')\n",
    "d_0 = np.vstack((d_0, np.zeros(g.num_cells)))\n",
    "pp.plot_grid(g, p_0, d_0, figsize=(8, 6), vector_scale=1/3, if_plot=False)\n",
    "plt.title(\"Initial condition\")\n",
    "for t in time_steps:\n",
    "    d = np.reshape(stored_displacements[t], (2, g.num_cells), 'F')\n",
    "    d = np.vstack((d, np.zeros(g.num_cells)))\n",
    "    pp.plot_grid(g, stored_pressures[t], d, figsize=(8, 6), vector_scale=10, if_plot=False)\n",
    "    plt.title(\"Time step {}\".format(str(t + 1)))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
